Could you please help me on the following ANCOVA issue?
This is a part of my dataset:
sampling dist h
1 wi 200 0.8687212
2 wi 200 0.8812909
3 wi 200 0.8267464
4 wi 0 0.8554508
5 wi 0 0.9506721
6 wi 0 0.8112781
7 wi 400 0.8687212
8 wi 400 0.8414646
9 wi 400 0.7601675
10 wi 900 0.6577048
11 wi 900 0.6098403
12 wi 900 0.5574382
13 sp 200 0.9149264
14 sp 200 0.9149264
15 sp 200 0.9248187
16 sp 0 0.9974016
17 sp 0 0.9997114
18 sp 0 0.8812909
...
h is the dependent variable, distance the covariate and sampling the factor.
the slopes for h~distance linear regressions are significantly different from 0
for all samplings
In order to compare the regression slopes for each sampling, i did an ANCOVA
with the ancova() function of the HH package:
>mod<-ancova(h~sampling*dist,data)
There was a significant interaction term:
Analysis of Variance Table
Response: h
Df Sum Sq Mean Sq F value Pr(>F)
sampling 3 0.22822 0.07607 13.7476 2.624e-06 ***
dist 1 0.51291 0.51291 92.6908 5.703e-12 ***
sampling:dist 3 0.05112 0.01704 3.0792 0.03822 *
Residuals 40 0.22134 0.00553
Because there exist significantly different regression slopes, I did a post hoc
test with glht() to find out between which samplings:
>summary(glht(mod, linfct=mcp(sampling="Tukey")))
The results seem to say that there are no significantly different slopes for
any of the pair-wise comparisons of factor levels:
Simultaneous Tests for General Linear Hypotheses
Multiple Comparisons of Means: Tukey Contrasts
Fit: aov(formula = h ~ sampling * dist, data = data)
Linear Hypotheses:
Estimate Std. Error z value Pr(>|z|)
sp - au == 0 0.06696 0.04562 1.468 0.457
su - au == 0 -0.02238 0.04562 -0.491 0.961
wi - au == 0 0.01203 0.04562 0.264 0.994
su - sp == 0 -0.08934 0.04562 -1.958 0.204
wi - sp == 0 -0.05493 0.04562 -1.204 0.624
wi - su == 0 0.03441 0.04562 0.754 0.875
(Adjusted p values reported -- single-step method)
Warning message:
In mcp2matrix(model, linfct = linfct) :
covariate interactions found -- default contrast might be inappropriate
My questions are:
- Did I make a mistake somewhere? (I probably did!)
- Could I do pairwise ANCOVAs and thus have just two factor levels (=two
regression slopes) to compare each time?
What does the warning message "covariate interactions found -- default contrast
might be inappropriate" mean?
Thank you!
Athanasios Evagelopoulos
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